Open AccessA stabilized nonconforming Nitsche's extended finite element method for Stokes interface problems
Author(s) -
Xiaoxiao He,
Fei Song,
Weibing Deng
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021163
Subject(s) - mathematics , norm (philosophy) , finite element method , combinatorics , mathematical analysis , physics , thermodynamics , political science , law
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The problem is written on mixed form using nonconforming \begin{document}$ P_1 $\end{document} velocity and elementwise \begin{document}$ P_0 $\end{document} pressure. Extra stabilization terms involving velocity and pressure are added in the discrete bilinear form. An inf-sup stability result is derived, which is uniform with respect to mesh size \begin{document}$ h $\end{document} , the viscosity and the position of the interface. An optimal priori error estimates are obtained. Moreover, the errors in energy norm for velocity and in \begin{document}$ L^2 $\end{document} norm for pressure are uniform to the viscosity and the location of the interface. Results of numerical experiments are presented to support the theoretical analysis.